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April 1st, 2010
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Issued by: Renesas Electronics Corporation (http://www.renesas.com)
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Notice
1.
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APPLICATION NOTE
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
Introduction
Produces the square root of a 32-bit binary number as a 16-bit binary number.
Target Device
H8/300H Tiny Series
Contents
1.
Function ............................................................................................................................................ 2
2.
Arguments......................................................................................................................................... 2
3.
Changes to Internal Registers and Flags ......................................................................................... 2
4.
Programming Specifications ............................................................................................................. 3
5.
Note................................................................................................................................................... 3
6.
Description ........................................................................................................................................ 4
7.
Flowchart........................................................................................................................................... 6
8.
Program Listing................................................................................................................................. 8
REJ06B0074-0200/Rev.2.00
June 2006
Page 1 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
1.
Function
1. Produces the square root of a 32-bit binary number as a 16-bit binary number.
2. Finds and outputs the square root of a 32-bit binary number as a 16-bit binary number.
3. The arguments are all unsigned integers. All data operations are on the general registers.
2.
Arguments
Input
Output
3.
Contents
Original number
(binary number for square-root extraction)
Square root
Storage Location
R4, R5
Data Length (Bytes)
4
R3
2
Changes to Internal Registers and Flags
31
16 15
8 7
ER0
Work
ER1
Work
ER2
Work
ER3
Result
ER4
Input
ER5
Input
0
Work
ER6
ER7 (SP)
: No change
I
UI
H
U
N
Z
V
C
: Varies
0 : Fixed to 0
1 : Fixed to 1
REJ06B0074-0200/Rev.2.00
June 2006
Page 2 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
4.
Programming Specifications
Program memory (bytes)
94
Data memory (bytes)
0
Stack (bytes)
0
Number of cycles
1340
Re-entrant
Yes
Relocatalbe
Yes
Interrupts during execution
Yes
5.
Note
The number of cycles in the programming specifications is the value in the execution of SQRT as shown in figure 1.
REJ06B0074-0200/Rev.2.00
June 2006
Page 3 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
6.
6.1
Description
Description of Functions
1. The arguments are as follows.
R4: Set the higher-order word of the original number in 32-bit binary here, as an input argument.
R5: Set the lower-order word of the original number here.
R3: The square root (16-bit binary) is set here, as an output argument.
2. The following figure illustrates the execution of the SQRT subroutine. When the input arguments are set as shown
below, the corresponding square root is set in R3.
R4
1
Input arguments
R4, R5
(H'FFFFFFFF)
Output argument
R3
(H'FFFF)
F
R5
F
F
F
F
F
F
F
F
F
R3
2
F
F
Figure 1 Example of SQRT Execution
6.2
Usage Notes
1. Any higher-order bits of the input argument that are unused must be explicitly set to "0", as shown in figure 2.
Otherwise, the correct result might not be obtained because undefined data in the higher-order bits is included in
computation of the square root.
R4
0
0
R5
0
F
F
F
F
F
F
F
R3
0
3
Figure 2 Example when Higher-order Bits are not Used
2. The fractional part of the result is discarded.
6.3
Description of Data Memory
No data memory is used by SQRT.
REJ06B0074-0200/Rev.2.00
June 2006
Page 4 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
6.4
Example of Usage
After setting the number for which the square root is to be extracted, call the SQRT subroutine.
WORK1
. RES. W 2
Reservation of the data memory area for setting by the user program of the 32-bit binary
number for square-root extraction.
WORK2
. RES. W 2
.
.
.
Reservation of a data memory area to hold the 16-bit binary square root for the user program.
MOV. W @WORK1, R4
Sets, as the input argument, the 32-bit binary number for square-root extraction that is specified
by the user program.
MOV. W @WORK1+2, R5
JSR
@SQRT
Subroutine call of SQRT.
Transfers , to the data memory of the user program, the 16-bit binary square root the output by
the subroutine.
MOV. W R3, @WORK 2
.
.
.
6.5
Principles of Operation
1. The following figure shows the method used to calculate the square root (H'05) of the hexadecimal number H'22.
C
A
1
1
B
10
0
0
10
0
1
1
α...... 10
1
0
D
1
10
1
E
0
00
1
00
0
1
F
1
10
(1) ......Square root
(2) ......Original number
00
10
10
01
(3)
(4)
(5)
(6)
(7)
10
01
(8)
Figure 3 Calculation of Square Root
1) As shown in the figure, the square root can be found by processing every two-bit unit, from highest to lowest
order, of the original number.
2) The square root (1) is equivalent to the quotient when α is divided by two. Parameter α is found through the
operations A, B, and C in the figure. The SQRT subroutine finds the square root by calculating the value of α
and then dividing it by two.
2. Details on the program are given below.
The program:
a) sets D'16 in R6L, which is the number of two-bit units in a 32-bit binary number;
b) clears the area for storage of the square root (R2, R3) and the working area (R0, R1);
c) extracts the two highest-order bits of the input binary number to R0 and R1, by rotating R4, R5, R0, and R1 two
bits to the left;
d) places "1" in R2, R3;
e) subtracts R2, R3 from R0, R1 to find the difference (D, (2), (3), and (4)), then sets difference thus found in R0,
R1; and
f) if the result is positive, increments R2, R3 (A to (4)); if the result is negative, decrements R2, R3, and adds R2,
R3 to R0, R1 (D, E, and (6)).
3. In SQRT, R6 is decremented each time steps c) through f) above are performed, and this processing is repeated until
R6 has reached "0".
REJ06B0074-0200/Rev.2.00
June 2006
Page 5 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
7.
Flowchart
SQRT
1
#D'16 → R6L
......
Load D'16 (number of times to repeat two-bit processing)
into the loop counter (R6L).
#H'0000 → R0
R0 → R1
R0 → R2
R0 → R3
......
Clear the working area (R0, R1) and calculation result
area (R2, R3).
......
Shift the original number 2 bits left to take out the upper
2-bit value. Rotate the working area 2 bits left to set the
lower 2 bits.
LBL1
#H'02 → R6H
LBL2
Shift R5L 1-bit left
Rotate R5H 1-bit left
Rotate R4L 1-bit left
Rotate R4H 1-bit left
Rotate R1L 1-bit left
Rotate R1H 1-bit left
Rotate R0L 1-bit left
Rotate R0H 1-bit left
R6H - #1 → R6H
No
R6H = 0
Yes
2
REJ06B0074-0200/Rev.2.00
June 2006
Page 6 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
2
1 → C flag
Rotate R3L 1-bit left
Rotate R3H 1-bit left
Rotate R2L 1-bit left
Rotate R2H 1-bit left
R1 - R3 → R1
R0L - R2L - C → R0L
R0H - R2H - C → R0H
......
Rotate the calculation-result area 1 bit left,
and set "1" in the LSB.
......
Subtract the value in the calculation-result area
from that in the working area, and set the result
in the working area. Branch if there is no borrow.
......
Add the value in the working area to that in the
calculation-result area,and restore the working
area's value.
......
Clear the LSB of the calculation-result area,
which was set to "1".
Yes
C=0
No
R1 + R3 → R1
R0L + R2L + C → R0L
R0H + R2H + C → R0H
1 → C flag
R3L - #H'00 - C → R3L
R3H - #H'00 - C → R3H
R2L - #H'00 - C → R2L
R2H - #H'00 - C → R2H
1 → C flag
R3L + #H'00 + C → R3L
R3H + #H'00 + C → R3H
R2L + #H'00 + C → R2L
R2H + #H'00 + C → R2H
......
Add "1" to the value in the calculation-result area.
......
Branch 16 times.
......
Divide the value in the calculation-result area
by 2 and take the result as the square root.
LBL4
R6L - #1 → R6L
LBL1 Yes
1
R6L ≠ 0
No
Shift R2H 1-bit right
Rotate R2L 1-bit right
Rotate R3H 1-bit right
Rotate R3L 1-bit right
RTS
REJ06B0074-0200/Rev.2.00
June 2006
Page 7 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
8.
Program Listing
1
1
;********************************************************************
2
2
;*
3
3
;*
4
4
;*
5
5
;********************************************************************
6
6
;*
7
7
;*
8
8
;*
*
NAME : 32 BIT SQUARE ROOT (SQRT)
*
*
*
ENTRY
: R4,R5
(32 BIT BINARY)
*
*
9
9
;*
10
10
;*
11
11
;********************************************************************
12
12
;
13
13
.CPU
300HN
14
.SECTION
SQRT_code,CODE,ALIGN=2
.EXPORT
SQRT
14
0000
15
15
16
16
;
SQRT
17
RETURNS : R3
(SQUARE ROOT)
*
*
00000000
17
.EQU
$
;Entry point
18
0000
FE10
18
MOV.B
#D'16,R6L
;Set shift counter
19
0002
79000000
19
MOV.W
#H'0000,R0
;Clear R0
20
0006
0D01
20
MOV.W
R0,R1
;Clear R1
21
0008
0D02
21
MOV.W
R0,R2
;Clear R2
22
000A
0D03
22
MOV.W
R0,R3
;Clear R3
23
000C
24
000C
MOV.B
#H'02,R6H
25
000E
26
000E
100D
26
SHLL.B
R5L
27
0010
1205
27
ROTXL.B
R5H
28
0012
120C
28
ROTXL.B
R4L
29
0014
1204
29
ROTXL.B
R4H
30
0016
1209
30
ROTXL.B
R1L
31
0018
1201
31
ROTXL.B
R1H
32
001A
1208
32
ROTXL.B
R0L
33
001C
1200
33
ROTXL.B
R0H
34
001E
1A06
34
DEC.B
R6H
35
0020
46EC
35
BNE
LBL2
;Branch if Z=0
36
0022
0401
36
ORC.B
#H'01,CCR
;Set C flag of CCR
37
0024
120B
37
ROTXL.B
R3L
;Rotate square root
38
0026
1203
38
ROTXL.B
R3H
39
0028
120A
39
ROTXL.B
R2L
40
002A
1202
40
ROTXL.B
R2H
41
002C
1931
41
SUB.W
R3,R1
;R1
42
002E
1EA8
42
SUBX.B
R2L,R0L
;R0L - R2L - C -> R0L
43
0030
1E20
43
SUBX.B
R2H,R0H
;R0H - R2H - C -> R0H
44
0032
4412
44
BCC
LBL3
;Branch if C=0
45
0034
0931
45
ADD.W
R3,R1
;R1
46
0036
0EA8
46
ADDX.B
R2L,R0L
;R0L + R2L + C -> R0L
47
0038
0E20
47
ADDX.B
R2H,R0H
;R0H + R2H + C -> R0H
48
003A
0401
48
ORC.B
#H'01,CCR
;Bit set C flag of CCR
49
003C
BB00
49
SUBX.B
#H'00,R3L
;R3L - #H'00 - C -> R3L
50
003E
B300
50
SUBX.B
#H'00,R3H
;R3H - #H'00 - C -> R3H
51
0040
BA00
51
SUBX.B
#H'00,R2L
;R2L - #H'00 - C -> R2L
52
0042
B200
52
SUBX.B
#H'00,R2H
;R2H - #H'00 - C -> R2H
23
F602
24
25
REJ06B0074-0200/Rev.2.00
LBL1
LBL2
June 2006
;Shift 32 bit binary 1 bit left
;Decrement R6H
- R3
+ R3
-> R1
-> R1
Page 8 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
53
0044
54
0046
400A
55
0046
0401
56
0048
9B00
57
004A
58
53
BRA
LBL4
;
55
ORC.B
#H'01,CCR
;Bit set C flag of CCR
56
ADDX.B
#H'00,R3L
;R3L + #H'00 + C -> R3L
9300
57
ADDX.B
#H'00,R3H
;R3H + #H'00 + C -> R3H
004C
9A00
58
ADDX.B
#H'00,R2L
;R2L + #H'00 + C -> R2L
59
004E
9200
59
ADDX.B
#H'00,R2H
;R2H + #H'00 + C -> R2H
60
0050
61
0050
61
DEC.B
R6L
;Decrement shift counter
62
0052
46B8
62
BNE
LBL1
;Branch if
63
0054
1102
63
SHLR.B
R2H
64
0056
130A
64
ROTXR.B
R2L
65
0058
1303
65
ROTXR.B
R3H
66
005A
130B
66
ROTXR.B
R3L
67
005C
5470
67
54
60
1A0E
68
68
69
69
*****
TOTAL ERRORS
*****
TOTAL WARNINGS 0
LBL3
LBL4
;Rotate square root
RTS
;
.END
0
REJ06B0074-0200/Rev.2.00
June 2006
Page 9 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
Revision Record
Rev.
2.00
Date
Jun.12.06
REJ06B0074-0200/Rev.2.00
Description
Page
Summary
—
Format has been changed from Hitachi version to Renesas
version.
June 2006
Page 10 of 11
H8/300H Tiny Series
Square Root of a 32-Bit Binary Number (SQRT)
Keep safety first in your circuit designs!
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Remember to give due consideration to safety when making your circuit designs, with appropriate
measures such as (i) placement of substitutive, auxiliary circuits, (ii) use of nonflammable material or
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REJ06B0074-0200/Rev.2.00
June 2006
Page 11 of 11